Open-ended tasks-- assignments with no single answer and/or no single method to determine an answer-- are one of the ways that I can teach math in a multi-age classroom, meeting everyone's developmental needs without running myself crazy. Many of the open-ended tasks I use are story problems like the peas and carrots question. (I have 7 veggies, some are peas and some are carrots. How many of each could I have?) Students generally solve these problems with pencil and paper, but with other open-ended tasks students might use varied methods. One of my favorite open-ended tasks is challenging the class to calculate the number of students in the school by adding up the students in each of our classrooms. To solve this problem students use snap cubes, draw pictures, group base ten blocks, as well as using the traditional addition algorithm.
Here are a few more examples of open-ended tasks that I might use with my 1st-2nd graders other than story problems:
solving pattern block puzzles with varied solutions
creating different coin combinations
recording equivalent number sentences using a number balance
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